Sufficient Condition Sample Clauses

Sufficient Condition. Since the goal of multi-oracle adversaries is to win any of the single-oracle games it is given, finding the optimal strategy is a question of targeting those single- oracle games for which it has the highest chance of winning, relative to its query allotment. The information that the adversary can work with is the transcripts produced from each single-oracle game and how many queries it has left. So, for example, a good strategy for an adversary might be to query each oracle once, and to estimate based on all of the transcripts which oracle is the weakest, and then to focus on the weakest one. Conversely, if all of the oracles are equally strong, then, intuitively, one might think that it does not make a difference that the adversary can work with more than one oracle, since there is little difference between the various oracles, and the adversary’s best strategy would seem to be to focus its effort on just one of them. However, to formally establish this we require an additional condition: it must be the case that when an optimal single-oracle adversary is given addi- tional knowledge about the oracle, then its chance of winning the game does not decrease relative to an optimal single-oracle adversary given less knowledge. Now, if an adversary is interacting with multiple oracles, and it has more infor- mation about one oracle over the others, then its best strategy is to stick to that oracle instead of switching to another one. This condition breaks down, for instance, if a construction has weak keys: if an adversary has the knowledge that its oracle is using a weak key, then it might have better advantage in winning the game versus an oracle where there is still a chance of interacting with a strong key. Below, we formalize the idea of giving adversaries additional knowledge via games with advice, which is equivalent to the concept of projected systems and their advantage by Xxˇxx and Xxxxxx [25]. Xxˇxx and Xxxxxx’x projected sys- tems explicitly define new conditional probability distributions which explain the behavior of the system from a given starting transcript. For our purposes we do not need to use the definition of a projected system directly, only the associated advantage definition. ∈ ∈ ∈ ×
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